Avocado Model Building Homework

#1 MVP We’ve looked at a few different ways in which we can build models this week, including how to prepare them properly. This weekend we’ll build a multiple linear regression model on a dataset which will need some preparation. The data has come from Kaggle and can be found in the data folder.

We want to model avocado sales. You’ll need to identify the target variable and use the tools we’ve worked with this week in order to prepare your dataset and find appropriate predictors. Once you’ve built your model use the validation techniques discussed on Wednesday to evaluate it.

#2 Extensions Build a decision tree to model the likelihood of a sale being of an organic avocado. Use k-means clustering to investigate potential relationships between the year and the average avocado price.

library(tidyverse)

Registered S3 method overwritten by 'dplyr':
  method           from
  print.rowwise_df     
── Attaching packages ─────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.2.0     ✔ purrr   0.3.2
✔ tibble  2.1.3     ✔ dplyr   0.8.2
✔ tidyr   0.8.3     ✔ stringr 1.4.0
✔ readr   1.3.1     ✔ forcats 0.4.0
── Conflicts ────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

#loading in data
avocado <- read.csv("data/avocado.csv")

# investigate structure and summary of data
str(avocado)

'data.frame':   18249 obs. of  14 variables:
 $ X           : int  0 1 2 3 4 5 6 7 8 9 ...
 $ Date        : Factor w/ 169 levels "2015-01-04","2015-01-11",..: 52 51 50 49 48 47 46 45 44 43 ...
 $ AveragePrice: num  1.33 1.35 0.93 1.08 1.28 1.26 0.99 0.98 1.02 1.07 ...
 $ Total.Volume: num  64237 54877 118220 78992 51040 ...
 $ X4046       : num  1037 674 795 1132 941 ...
 $ X4225       : num  54455 44639 109150 71976 43838 ...
 $ X4770       : num  48.2 58.3 130.5 72.6 75.8 ...
 $ Total.Bags  : num  8697 9506 8145 5811 6184 ...
 $ Small.Bags  : num  8604 9408 8042 5677 5986 ...
 $ Large.Bags  : num  93.2 97.5 103.1 133.8 197.7 ...
 $ XLarge.Bags : num  0 0 0 0 0 0 0 0 0 0 ...
 $ type        : Factor w/ 2 levels "conventional",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ year        : int  2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 ...
 $ region      : Factor w/ 54 levels "Albany","Atlanta",..: 1 1 1 1 1 1 1 1 1 1 ...

summary(avocado)

       X                 Date        AveragePrice    Total.Volume     
 Min.   : 0.00   2015-01-04:  108   Min.   :0.440   Min.   :      85  
 1st Qu.:10.00   2015-01-11:  108   1st Qu.:1.100   1st Qu.:   10839  
 Median :24.00   2015-01-18:  108   Median :1.370   Median :  107377  
 Mean   :24.23   2015-01-25:  108   Mean   :1.406   Mean   :  850644  
 3rd Qu.:38.00   2015-02-01:  108   3rd Qu.:1.660   3rd Qu.:  432962  
 Max.   :52.00   2015-02-08:  108   Max.   :3.250   Max.   :62505647  
                 (Other)   :17601                                     
     X4046              X4225              X4770           Total.Bags      
 Min.   :       0   Min.   :       0   Min.   :      0   Min.   :       0  
 1st Qu.:     854   1st Qu.:    3009   1st Qu.:      0   1st Qu.:    5089  
 Median :    8645   Median :   29061   Median :    185   Median :   39744  
 Mean   :  293008   Mean   :  295155   Mean   :  22840   Mean   :  239639  
 3rd Qu.:  111020   3rd Qu.:  150207   3rd Qu.:   6243   3rd Qu.:  110783  
 Max.   :22743616   Max.   :20470573   Max.   :2546439   Max.   :19373134  
                                                                           
   Small.Bags         Large.Bags       XLarge.Bags                 type     
 Min.   :       0   Min.   :      0   Min.   :     0.0   conventional:9126  
 1st Qu.:    2849   1st Qu.:    127   1st Qu.:     0.0   organic     :9123  
 Median :   26363   Median :   2648   Median :     0.0                      
 Mean   :  182195   Mean   :  54338   Mean   :  3106.4                      
 3rd Qu.:   83338   3rd Qu.:  22029   3rd Qu.:   132.5                      
 Max.   :13384587   Max.   :5719097   Max.   :551693.7                      
                                                                            
      year                      region     
 Min.   :2015   Albany             :  338  
 1st Qu.:2015   Atlanta            :  338  
 Median :2016   BaltimoreWashington:  338  
 Mean   :2016   Boise              :  338  
 3rd Qu.:2017   Boston             :  338  
 Max.   :2018   BuffaloRochester   :  338  
                (Other)            :16221  

# check for missing values
apply(avocado, 2, function(x) any(is.na(x) | is.infinite(x) | is.null(x)))

           X         Date AveragePrice Total.Volume        X4046        X4225 
       FALSE        FALSE        FALSE        FALSE        FALSE        FALSE 
       X4770   Total.Bags   Small.Bags   Large.Bags  XLarge.Bags         type 
       FALSE        FALSE        FALSE        FALSE        FALSE        FALSE 
        year       region 
       FALSE        FALSE 

# get rid of spaces in column names
names(avocado) <- make.names(names(avocado))

# make all column names lower case
for( i in colnames(avocado)) {
  colnames(avocado)[which(colnames(avocado) == i)] = tolower(i)
}

avocado

library(lubridate)

Attaching package: ‘lubridate’

The following object is masked from ‘package:base’:

    date

avocado$year <- year(ymd(as.character(avocado$date)))

avocado$month <- month(ymd(as.character(avocado$date)))

avocado$week <- week(ymd(as.character(avocado$date)))

glimpse(avocado)

Observations: 18,249
Variables: 16
$ x            <int> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18…
$ date         <fct> 2015-12-27, 2015-12-20, 2015-12-13, 2015-12-06, 2015-11-29, 2015…
$ averageprice <dbl> 1.33, 1.35, 0.93, 1.08, 1.28, 1.26, 0.99, 0.98, 1.02, 1.07, 1.12…
$ total.volume <dbl> 64236.62, 54876.98, 118220.22, 78992.15, 51039.60, 55979.78, 834…
$ x4046        <dbl> 1036.74, 674.28, 794.70, 1132.00, 941.48, 1184.27, 1368.92, 703.…
$ x4225        <dbl> 54454.85, 44638.81, 109149.67, 71976.41, 43838.39, 48067.99, 736…
$ x4770        <dbl> 48.16, 58.33, 130.50, 72.58, 75.78, 43.61, 93.26, 80.00, 85.34, …
$ total.bags   <dbl> 8696.87, 9505.56, 8145.35, 5811.16, 6183.95, 6683.91, 8318.86, 6…
$ small.bags   <dbl> 8603.62, 9408.07, 8042.21, 5677.40, 5986.26, 6556.47, 8196.81, 6…
$ large.bags   <dbl> 93.25, 97.49, 103.14, 133.76, 197.69, 127.44, 122.05, 562.37, 28…
$ xlarge.bags  <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
$ type         <fct> conventional, conventional, conventional, conventional, conventi…
$ year         <dbl> 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015…
$ region       <fct> Albany, Albany, Albany, Albany, Albany, Albany, Albany, Albany, …
$ month        <dbl> 12, 12, 12, 12, 11, 11, 11, 11, 11, 10, 10, 10, 10, 9, 9, 9, 9, …
$ week         <dbl> 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, …

avocado %>%
  ggplot(aes(x = averageprice)) +
  geom_histogram() +
  facet_wrap(~ year)

# seems to be less data in 2018 compared to other years 

#table(avocado$year)

avocado %>%
  ggplot(aes(x = averageprice, fill = type)) +
  geom_histogram() +
  facet_wrap(~ month)

#table(avocado$month)

avocado %>%
  ggplot(aes(x = averageprice, fill = type)) +
  geom_histogram() +
  facet_wrap(~ week)

#table(avocado$week)

avocado %>%
  ggplot(aes(x = as.factor(year), y = averageprice, group = year)) +
  geom_boxplot()

avocado %>%
  ggplot(aes(x = as.factor(month), y = averageprice, group = month)) +
  geom_boxplot()

avocado %>%
  ggplot(aes(x = as.factor(type), y = averageprice)) +
  geom_boxplot() +
  coord_flip()

#must greater spread of prices for organic

var(avocado$averageprice)

[1] 0.1621484

mean(avocado$averageprice)

[1] 1.405978

sd(avocado$averageprice)

[1] 0.4026766

#assuming normally distributed averageprice
#approx 68 percent of avocados in our data sold at prices between $1.405978 - $0.4026766 = $1.003302 and $1.405978 + $0.4026766 = $1.808655

mean(avocado$averageprice) - sd(avocado$averageprice)

[1] 1.003302

mean(avocado$averageprice) + sd(avocado$averageprice)

[1] 1.808655

avocado %>%
  ggplot(aes(x = averageprice, fill = type)) +
  geom_histogram()

avocado %>%
  ggplot(aes(x = averageprice, fill = type)) +
  geom_histogram() +
  facet_wrap(~ type)

#more conventional than organic sold but at generally lower price.

avocado %>%
  ggplot(aes(x = region, y = averageprice, color = as.factor(year))) +
  geom_point() +
  coord_flip() +
  facet_wrap(~ year)

# great deal of variability of price around region

avocado %>%
  ggplot(aes(x = region, y = averageprice, color = as.factor(month))) +
  geom_point() +
  coord_flip() +
  facet_wrap(~ month)

# great deal of variability of price around region and month

avocado %>%
  ggplot(aes(x = region, y = averageprice, color = as.factor(year))) +
  geom_point() +
  coord_flip() +
  facet_wrap(~ type)

# and variability around year too

avocado %>%
  ggplot(aes(x = ymd(as.character(avocado$date)), y = averageprice, color = type)) +
  geom_line() +
  facet_wrap(~ type, ncol = 1)

region_table <- table(avocado$region)
round(prop.table(region_table) *100, digits = 1)

             Albany             Atlanta BaltimoreWashington               Boise 
                1.9                 1.9                 1.9                 1.9 
             Boston    BuffaloRochester          California           Charlotte 
                1.9                 1.9                 1.9                 1.9 
            Chicago    CincinnatiDayton            Columbus       DallasFtWorth 
                1.9                 1.9                 1.9                 1.9 
             Denver             Detroit         GrandRapids          GreatLakes 
                1.9                 1.9                 1.9                 1.9 
 HarrisburgScranton HartfordSpringfield             Houston        Indianapolis 
                1.9                 1.9                 1.9                 1.9 
       Jacksonville            LasVegas          LosAngeles          Louisville 
                1.9                 1.9                 1.9                 1.9 
  MiamiFtLauderdale            Midsouth           Nashville    NewOrleansMobile 
                1.9                 1.9                 1.9                 1.9 
            NewYork           Northeast  NorthernNewEngland             Orlando 
                1.9                 1.9                 1.9                 1.9 
       Philadelphia       PhoenixTucson          Pittsburgh              Plains 
                1.9                 1.9                 1.9                 1.9 
           Portland   RaleighGreensboro     RichmondNorfolk             Roanoke 
                1.9                 1.9                 1.9                 1.9 
         Sacramento            SanDiego        SanFrancisco             Seattle 
                1.9                 1.9                 1.9                 1.9 
      SouthCarolina        SouthCentral           Southeast             Spokane 
                1.9                 1.9                 1.9                 1.9 
            StLouis            Syracuse               Tampa             TotalUS 
                1.9                 1.9                 1.9                 1.9 
               West    WestTexNewMexico 
                1.9                 1.8 

type_table <- table(avocado$type)
round(prop.table(type_table) * 100, digits = 1)

conventional      organic 
          50           50 

table(avocado$year)

2015 2016 2017 2018 
5615 5616 5722 1296 

summary(avocado)

       x                 date        averageprice    total.volume     
 Min.   : 0.00   2015-01-04:  108   Min.   :0.440   Min.   :      85  
 1st Qu.:10.00   2015-01-11:  108   1st Qu.:1.100   1st Qu.:   10839  
 Median :24.00   2015-01-18:  108   Median :1.370   Median :  107377  
 Mean   :24.23   2015-01-25:  108   Mean   :1.406   Mean   :  850644  
 3rd Qu.:38.00   2015-02-01:  108   3rd Qu.:1.660   3rd Qu.:  432962  
 Max.   :52.00   2015-02-08:  108   Max.   :3.250   Max.   :62505647  
                 (Other)   :17601                                     
     x4046              x4225              x4770           total.bags      
 Min.   :       0   Min.   :       0   Min.   :      0   Min.   :       0  
 1st Qu.:     854   1st Qu.:    3009   1st Qu.:      0   1st Qu.:    5089  
 Median :    8645   Median :   29061   Median :    185   Median :   39744  
 Mean   :  293008   Mean   :  295155   Mean   :  22840   Mean   :  239639  
 3rd Qu.:  111020   3rd Qu.:  150207   3rd Qu.:   6243   3rd Qu.:  110783  
 Max.   :22743616   Max.   :20470573   Max.   :2546439   Max.   :19373134  
                                                                           
   small.bags         large.bags       xlarge.bags                 type     
 Min.   :       0   Min.   :      0   Min.   :     0.0   conventional:9126  
 1st Qu.:    2849   1st Qu.:    127   1st Qu.:     0.0   organic     :9123  
 Median :   26363   Median :   2648   Median :     0.0                      
 Mean   :  182195   Mean   :  54338   Mean   :  3106.4                      
 3rd Qu.:   83338   3rd Qu.:  22029   3rd Qu.:   132.5                      
 Max.   :13384587   Max.   :5719097   Max.   :551693.7                      
                                                                            
      year                      region          month             week      
 Min.   :2015   Albany             :  338   Min.   : 1.000   Min.   : 1.00  
 1st Qu.:2015   Atlanta            :  338   1st Qu.: 3.000   1st Qu.:11.00  
 Median :2016   BaltimoreWashington:  338   Median : 6.000   Median :25.00  
 Mean   :2016   Boise              :  338   Mean   : 6.177   Mean   :25.24  
 3rd Qu.:2017   Boston             :  338   3rd Qu.: 9.000   3rd Qu.:39.00  
 Max.   :2018   BuffaloRochester   :  338   Max.   :12.000   Max.   :53.00  
                (Other)            :16221                                   

library(psych)

pairs.panels(avocado[c("averageprice", "x4046", "x4225", "x4770", "small.bags", "large.bags", "xlarge.bags", "type", "region", "month", "week", "year")])

summary(avocado)

       x                 date        averageprice    total.volume     
 Min.   : 0.00   2015-01-04:  108   Min.   :0.440   Min.   :      85  
 1st Qu.:10.00   2015-01-11:  108   1st Qu.:1.100   1st Qu.:   10839  
 Median :24.00   2015-01-18:  108   Median :1.370   Median :  107377  
 Mean   :24.23   2015-01-25:  108   Mean   :1.406   Mean   :  850644  
 3rd Qu.:38.00   2015-02-01:  108   3rd Qu.:1.660   3rd Qu.:  432962  
 Max.   :52.00   2015-02-08:  108   Max.   :3.250   Max.   :62505647  
                 (Other)   :17601                                     
     x4046              x4225              x4770           total.bags      
 Min.   :       0   Min.   :       0   Min.   :      0   Min.   :       0  
 1st Qu.:     854   1st Qu.:    3009   1st Qu.:      0   1st Qu.:    5089  
 Median :    8645   Median :   29061   Median :    185   Median :   39744  
 Mean   :  293008   Mean   :  295155   Mean   :  22840   Mean   :  239639  
 3rd Qu.:  111020   3rd Qu.:  150207   3rd Qu.:   6243   3rd Qu.:  110783  
 Max.   :22743616   Max.   :20470573   Max.   :2546439   Max.   :19373134  
                                                                           
   small.bags         large.bags       xlarge.bags                 type     
 Min.   :       0   Min.   :      0   Min.   :     0.0   conventional:9126  
 1st Qu.:    2849   1st Qu.:    127   1st Qu.:     0.0   organic     :9123  
 Median :   26363   Median :   2648   Median :     0.0                      
 Mean   :  182195   Mean   :  54338   Mean   :  3106.4                      
 3rd Qu.:   83338   3rd Qu.:  22029   3rd Qu.:   132.5                      
 Max.   :13384587   Max.   :5719097   Max.   :551693.7                      
                                                                            
      year                      region          month             week      
 Min.   :2015   Albany             :  338   Min.   : 1.000   Min.   : 1.00  
 1st Qu.:2015   Atlanta            :  338   1st Qu.: 3.000   1st Qu.:11.00  
 Median :2016   BaltimoreWashington:  338   Median : 6.000   Median :25.00  
 Mean   :2016   Boise              :  338   Mean   : 6.177   Mean   :25.24  
 3rd Qu.:2017   Boston             :  338   3rd Qu.: 9.000   3rd Qu.:39.00  
 Max.   :2018   BuffaloRochester   :  338   Max.   :12.000   Max.   :53.00  
                (Other)            :16221                                   

# tidy up data
avocado_tidy <- avocado %>%
  select(-c("x", "date", "total.volume", "total.bags"))

glimpse(avocado_tidy)

Observations: 18,249
Variables: 12
$ averageprice <dbl> 1.33, 1.35, 0.93, 1.08, 1.28, 1.26, 0.99, 0.98, 1.02, 1.07, 1.12…
$ x4046        <dbl> 1036.74, 674.28, 794.70, 1132.00, 941.48, 1184.27, 1368.92, 703.…
$ x4225        <dbl> 54454.85, 44638.81, 109149.67, 71976.41, 43838.39, 48067.99, 736…
$ x4770        <dbl> 48.16, 58.33, 130.50, 72.58, 75.78, 43.61, 93.26, 80.00, 85.34, …
$ small.bags   <dbl> 8603.62, 9408.07, 8042.21, 5677.40, 5986.26, 6556.47, 8196.81, 6…
$ large.bags   <dbl> 93.25, 97.49, 103.14, 133.76, 197.69, 127.44, 122.05, 562.37, 28…
$ xlarge.bags  <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
$ type         <fct> conventional, conventional, conventional, conventional, conventi…
$ year         <dbl> 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015, 2015…
$ region       <fct> Albany, Albany, Albany, Albany, Albany, Albany, Albany, Albany, …
$ month        <dbl> 12, 12, 12, 12, 11, 11, 11, 11, 11, 10, 10, 10, 10, 9, 9, 9, 9, …
$ week         <dbl> 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, …

# x is just reference so no predictive power, taken out date as I have year, week and month. total.volume and total.bags can be derived
# from the other data

# changing type to logical as there are only two types of avocado - didn't bother with this as noticed the model did all of this automatically.
#avocado_tidy$is.organic <- with(avocado_tidy, type=="organic")

# using alias to check is there are any aliased vairables | this result (I assume) means no aliased variables
alias(averageprice ~ ., data = avocado_tidy)

Model :
averageprice ~ x4046 + x4225 + x4770 + small.bags + large.bags + 
    xlarge.bags + type + year + region + month + week

avocado_tidy %>%
  ggplot(aes(x = averageprice, y = type)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE)

library(caret)

Loading required package: lattice
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

Attaching package: ‘caret’

The following object is masked from ‘package:purrr’:

    lift

# using K-fold cross validation
# using 10 folds
# first model has everything included!
cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)

model <- train(averageprice ~ ., data = avocado_tidy,
               trControl = cv_10_fold,
               method = "lm")

model$pred

model$resample

mean(model$resample$RMSE)

[1] 0.2581192

mean(model$resample$Rsquared)

[1] 0.589387

summary(model)

Call:
lm(formula = .outcome ~ ., data = dat)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03539 -0.15729 -0.00504  0.14804  1.51228 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)               -1.061e+02  4.269e+00 -24.849  < 2e-16 ***
x4046                      1.034e-08  5.752e-09   1.799 0.072083 .  
x4225                     -1.084e-08  6.790e-09  -1.597 0.110331    
x4770                     -3.255e-09  4.421e-08  -0.074 0.941308    
small.bags                -1.777e-08  1.206e-08  -1.474 0.140629    
large.bags                -6.559e-08  2.101e-08  -3.121 0.001803 ** 
xlarge.bags                1.365e-06  2.037e-07   6.702 2.12e-11 ***
typeorganic                4.921e-01  4.036e-03 121.909  < 2e-16 ***
year                       5.321e-02  2.117e-03  25.135  < 2e-16 ***
regionAtlanta             -2.228e-01  1.985e-02 -11.224  < 2e-16 ***
regionBaltimoreWashington -2.373e-02  1.987e-02  -1.194 0.232363    
regionBoise               -2.131e-01  1.983e-02 -10.746  < 2e-16 ***
regionBoston              -2.727e-02  1.986e-02  -1.373 0.169619    
regionBuffaloRochester    -4.383e-02  1.983e-02  -2.210 0.027107 *  
regionCalifornia          -1.736e-01  2.028e-02  -8.559  < 2e-16 ***
regionCharlotte            4.526e-02  1.984e-02   2.282 0.022522 *  
regionChicago             -2.472e-03  1.994e-02  -0.124 0.901307    
regionCincinnatiDayton    -3.495e-01  1.985e-02 -17.608  < 2e-16 ***
regionColumbus            -3.090e-01  1.983e-02 -15.578  < 2e-16 ***
regionDallasFtWorth       -4.763e-01  1.987e-02 -23.968  < 2e-16 ***
regionDenver              -3.335e-01  1.995e-02 -16.713  < 2e-16 ***
regionDetroit             -2.906e-01  1.987e-02 -14.624  < 2e-16 ***
regionGrandRapids         -5.871e-02  1.984e-02  -2.960 0.003082 ** 
regionGreatLakes          -2.265e-01  2.047e-02 -11.069  < 2e-16 ***
regionHarrisburgScranton  -4.756e-02  1.983e-02  -2.398 0.016482 *  
regionHartfordSpringfield  2.587e-01  1.984e-02  13.043  < 2e-16 ***
regionHouston             -5.112e-01  1.987e-02 -25.734  < 2e-16 ***
regionIndianapolis        -2.469e-01  1.983e-02 -12.448  < 2e-16 ***
regionJacksonville        -5.003e-02  1.983e-02  -2.522 0.011665 *  
regionLasVegas            -1.785e-01  1.984e-02  -8.997  < 2e-16 ***
regionLosAngeles          -3.555e-01  2.015e-02 -17.644  < 2e-16 ***
regionLouisville          -2.741e-01  1.983e-02 -13.821  < 2e-16 ***
regionMiamiFtLauderdale   -1.326e-01  1.986e-02  -6.678 2.49e-11 ***
regionMidsouth            -1.472e-01  2.003e-02  -7.350 2.06e-13 ***
regionNashville           -3.491e-01  1.983e-02 -17.603  < 2e-16 ***
regionNewOrleansMobile    -2.584e-01  1.984e-02 -13.026  < 2e-16 ***
regionNewYork              1.746e-01  2.002e-02   8.721  < 2e-16 ***
regionNortheast            6.281e-02  2.145e-02   2.929 0.003407 ** 
regionNorthernNewEngland  -8.176e-02  1.984e-02  -4.121 3.79e-05 ***
regionOrlando             -5.500e-02  1.984e-02  -2.772 0.005570 ** 
regionPhiladelphia         7.308e-02  1.984e-02   3.683 0.000231 ***
regionPhoenixTucson       -3.355e-01  1.989e-02 -16.867  < 2e-16 ***
regionPittsburgh          -1.966e-01  1.983e-02  -9.915  < 2e-16 ***
regionPlains              -1.258e-01  1.989e-02  -6.328 2.54e-10 ***
regionPortland            -2.399e-01  1.985e-02 -12.083  < 2e-16 ***
regionRaleighGreensboro   -5.601e-03  1.984e-02  -0.282 0.777695    
regionRichmondNorfolk     -2.697e-01  1.983e-02 -13.600  < 2e-16 ***
regionRoanoke             -3.132e-01  1.983e-02 -15.791  < 2e-16 ***
regionSacramento           6.037e-02  1.983e-02   3.044 0.002337 ** 
regionSanDiego            -1.623e-01  1.984e-02  -8.183 2.96e-16 ***
regionSanFrancisco         2.444e-01  1.985e-02  12.312  < 2e-16 ***
regionSeattle             -1.148e-01  1.985e-02  -5.784 7.43e-09 ***
regionSouthCarolina       -1.579e-01  1.984e-02  -7.963 1.78e-15 ***
regionSouthCentral        -4.613e-01  2.053e-02 -22.466  < 2e-16 ***
regionSoutheast           -1.614e-01  2.038e-02  -7.920 2.51e-15 ***
regionSpokane             -1.154e-01  1.983e-02  -5.819 6.03e-09 ***
regionStLouis             -1.309e-01  1.983e-02  -6.600 4.23e-11 ***
regionSyracuse            -4.080e-02  1.983e-02  -2.058 0.039646 *  
regionTampa               -1.521e-01  1.984e-02  -7.664 1.89e-14 ***
regionTotalUS             -1.879e-01  2.446e-02  -7.685 1.61e-14 ***
regionWest                -2.554e-01  2.067e-02 -12.355  < 2e-16 ***
regionWestTexNewMexico    -2.962e-01  1.992e-02 -14.873  < 2e-16 ***
month                     -2.037e-02  6.578e-03  -3.097 0.001956 ** 
week                       9.460e-03  1.500e-03   6.307 2.90e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2578 on 18185 degrees of freedom
Multiple R-squared:  0.5916,    Adjusted R-squared:  0.5902 
F-statistic: 418.1 on 63 and 18185 DF,  p-value: < 2.2e-16

model <- lm(averageprice ~ ., data = avocado_tidy)
par(mfrow = c(2, 2))
plot(model)

looking for a lower error (RMSE) and a higher R squared value

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# much simpler model
model1 <- train(averageprice ~ type + region, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model1$resample$RMSE)

[1] 0.2716248

mean(model1$resample$Rsquared)

[1] 0.5450222

wrong direction

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# even simpler
model2 <- train(averageprice ~ type, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model2$resample$RMSE)

[1] 0.3172512

mean(model2$resample$Rsquared)

[1] 0.3793824

even worse

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)

model3 <- train(averageprice ~ type + month, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model3$resample$RMSE)

[1] 0.3104094

mean(model3$resample$Rsquared)

[1] 0.4058502

error reduced slightly and R squared increased

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)

model4 <- train(averageprice ~ type + year + region + week + month, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model4$resample$RMSE)

[1] 0.2585822

mean(model4$resample$Rsquared)

[1] 0.5873909

error reduced slightly further and R squared increased quite a bit

model4$resample

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)

model5 <- train(log(averageprice) ~ type + year + region + week + month, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model5$resample$RMSE)

[1] 0.1828857

mean(model5$resample$Rsquared)

[1] 0.6015081

model5 <- lm(log(averageprice) ~ type + year + region + week + month, 
                data = avocado_tidy)

model5$resample

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)

model6 <- train(log(averageprice) ~ type + year + region + week + month + region:type, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model6$resample$RMSE)

[1] 0.1730975

mean(model6$resample$Rsquared)

[1] 0.6432118

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# adding an interaction
model7 <- train(log(averageprice) ~ type + year + region + week + month + region:type + region:month, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model7$resample$RMSE)

[1] 0.1713983

mean(model7$resample$Rsquared)

[1] 0.6501079

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# adding a further interaction
model8 <- train(log(averageprice) ~ type + year + region + week + month + region:type + region:week, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model8$resample$RMSE)

[1] 0.1714282

mean(model8$resample$Rsquared)

[1] 0.6498005

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# adding a further interaction
model9 <- train(log(averageprice) ~ type + year + region + week + month + large.bags + region:type + region:week, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model9$resample$RMSE)

[1] 0.1710473

mean(model9$resample$Rsquared)

[1] 0.6515074

model9 <- lm(log(averageprice) ~ type + year + region + week + month + large.bags + region:type + region:week, 
                data = avocado_tidy)

cv_10_fold <- trainControl(method = "cv", number = 10, savePredictions = TRUE)
# adding a further interaction
model10 <- train(log(averageprice) ~ type + year + region + week + month + large.bags + x4046 + region:type + region:week, 
                data = avocado_tidy,
                trControl = cv_10_fold,
                method = "lm")

mean(model10$resample$RMSE)

[1] 0.1706929

mean(model10$resample$Rsquared)

[1] 0.6529101

model_best <- lm(log(averageprice) ~ type + year + region + week + month + large.bags + region:type + region:week, data = avocado_tidy)

broom::glance(model_best)

broom::glance(model5)

library(glmulti)
glmulti_fit <- glmulti(log(averageprice) ~ ., 
                       data = avocado_tidy,
                       level = 1,
                       minsize = 0,
                       maxsize = -1,
                       marginality = TRUE,
                       method = "g",
                       crit = bic,
                       confsetsize = 50,
                       fitfunction = lm)

Initialization...
TASK: Genetic algorithm in the candidate set.
Initialization...
Algorithm started...

After 10 generations:
Best model: log(averageprice)~1+type+region+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9854.10799286624
Mean crit= -7120.4009082924
Change in best IC: -19854.1079928662 / Change in mean IC: -17120.4009082924

After 20 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -7619.78735027147

Change in best IC: -11.3610586122322 / Change in mean IC: -499.386441979072

After 30 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -8428.39060430681

Change in best IC: 0 / Change in mean IC: -808.603254035344

After 40 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9091.57582938835

Change in best IC: 0 / Change in mean IC: -663.185225081537

After 50 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9269.99629809053

Change in best IC: 0 / Change in mean IC: -178.420468702187

After 60 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9356.53895117772

Change in best IC: 0 / Change in mean IC: -86.54265308719

After 70 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9413.99761573878

Change in best IC: 0 / Change in mean IC: -57.4586645610561

After 80 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9463.84807839402

Change in best IC: 0 / Change in mean IC: -49.8504626552422

After 90 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9494.96463126167

Change in best IC: 0 / Change in mean IC: -31.1165528676447

After 100 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9510.20790224408

Change in best IC: 0 / Change in mean IC: -15.2432709824134

After 110 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9564.90889652745

Change in best IC: 0 / Change in mean IC: -54.7009942833665

After 120 generations:
Best model: log(averageprice)~1+type+region+x4046+x4225+x4770+large.bags+xlarge.bags+year+month+week
Crit= -9865.46905147847
Mean crit= -9601.89315577691

Change in best IC: 0 / Change in mean IC: -36.9842592494606

After 130 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9652.65713922838

Change in best IC: -0.527765720667958 / Change in mean IC: -50.7639834514757

After 140 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9713.29155975643

Change in best IC: 0 / Change in mean IC: -60.6344205280475

After 150 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9735.1714615509

Change in best IC: 0 / Change in mean IC: -21.8799017944639

After 160 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9765.45787331366

Change in best IC: 0 / Change in mean IC: -30.2864117627687

After 170 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9786.43510135894

Change in best IC: 0 / Change in mean IC: -20.977228045278

After 180 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9797.54108235478

Change in best IC: 0 / Change in mean IC: -11.1059809958351

After 190 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9799.6766509245

Change in best IC: 0 / Change in mean IC: -2.13556856972355

After 200 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9805.1608054835

Change in best IC: 0 / Change in mean IC: -5.48415455900067

After 210 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9808.68707314903

Change in best IC: 0 / Change in mean IC: -3.52626766553112

After 220 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9808.68707314903

Change in best IC: 0 / Change in mean IC: 0

After 230 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9809.3312566835

Change in best IC: 0 / Change in mean IC: -0.644183534470358

After 240 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9809.3312566835

Change in best IC: 0 / Change in mean IC: 0

After 250 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9812.29568504222

Change in best IC: 0 / Change in mean IC: -2.96442835871312

After 260 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9813.67409702215

Change in best IC: 0 / Change in mean IC: -1.3784119799293

After 270 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9813.67409702215

Change in best IC: 0 / Change in mean IC: 0

After 280 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9815.26742080488

Change in best IC: 0 / Change in mean IC: -1.59332378273939

After 290 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9816.42032581553

Change in best IC: 0 / Change in mean IC: -1.15290501064919

After 300 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9816.42032581553

Change in best IC: 0 / Change in mean IC: 0

After 310 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9816.42032581553

Change in best IC: 0 / Change in mean IC: 0

After 320 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9819.28945251976

Change in best IC: 0 / Change in mean IC: -2.86912670423044

After 330 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9820.24869697667

Change in best IC: 0 / Change in mean IC: -0.959244456907982

After 340 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9820.54293535552

Change in best IC: 0 / Change in mean IC: -0.294238378852242

After 350 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9821.0397590408

Change in best IC: 0 / Change in mean IC: -0.496823685278287

After 360 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9824.24244444793

Change in best IC: 0 / Change in mean IC: -3.20268540712641

After 370 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9824.50650339013

Change in best IC: 0 / Change in mean IC: -0.264058942197153

After 380 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9824.50650339013

Change in best IC: 0 / Change in mean IC: 0

After 390 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9824.50650339013

Change in best IC: 0 / Change in mean IC: 0

After 400 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9824.50650339013

Change in best IC: 0 / Change in mean IC: 0

After 410 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9825.13468989543

Change in best IC: 0 / Change in mean IC: -0.628186505307895

After 420 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9825.13468989543

Change in best IC: 0 / Change in mean IC: 0

After 430 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9826.51298871173

Change in best IC: 0 / Change in mean IC: -1.37829881629477

After 440 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9827.70878641298

Change in best IC: 0 / Change in mean IC: -1.19579770125347

After 450 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9828.74488119945

Change in best IC: 0 / Change in mean IC: -1.03609478646285

After 460 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9832.36147166621

Change in best IC: 0 / Change in mean IC: -3.61659046676323

After 470 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9832.36147166621

Change in best IC: 0 / Change in mean IC: 0

After 480 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9832.43269613371

Change in best IC: 0 / Change in mean IC: -0.0712244675014517

After 490 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.46140983292

Change in best IC: 0 / Change in mean IC: -1.02871369921195

After 500 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.46140983292

Change in best IC: 0 / Change in mean IC: 0

After 510 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.46140983292

Change in best IC: 0 / Change in mean IC: 0

After 520 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.59954567518

Change in best IC: 0 / Change in mean IC: -0.138135842256816

After 530 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.59954567518

Change in best IC: 0 / Change in mean IC: 0

After 540 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9833.59954567518

Change in best IC: 0 / Change in mean IC: 0

After 550 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9834.12051676081

Change in best IC: 0 / Change in mean IC: -0.520971085634301

After 560 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.17682075758

Change in best IC: 0 / Change in mean IC: -1.05630399676375

After 570 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.17682075758

Change in best IC: 0 / Change in mean IC: 0

After 580 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.17682075758

Change in best IC: 0 / Change in mean IC: 0

After 590 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.17682075758

Change in best IC: 0 / Change in mean IC: 0

After 600 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.17682075758

Change in best IC: 0 / Change in mean IC: 0

After 610 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.3091603391

Change in best IC: 0 / Change in mean IC: -0.132339581523411

After 620 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.3091603391

Change in best IC: 0 / Change in mean IC: 0

After 630 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.3091603391

Change in best IC: 0 / Change in mean IC: 0

After 640 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Change in best IC: 0 / Change in mean IC: -0.0534448387115845

After 650 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Change in best IC: 0 / Change in mean IC: 0

After 660 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Change in best IC: 0 / Change in mean IC: 0

After 670 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Change in best IC: 0 / Change in mean IC: 0

After 680 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Change in best IC: 0 / Change in mean IC: 0

After 690 generations:
Best model: log(averageprice)~1+type+region+x4046+large.bags+xlarge.bags+year+month+week
Crit= -9865.99681719914
Mean crit= -9835.36260517781

Improvements in best and average IC have bebingo en below the specified goals.
Algorithm is declared to have converged.
Completed.